An adjustment arrangement of this type is disclosed in DE-OS No. 3336120. This discloses an adjustment member arranged between the brake piston and the hand brake piston, when a wear-dependent removal of material from the braking surfaces occurs, so that the hand brake application as well as the hydraulically actuated foot brake remain unchanged with the necessary play provided. Both pistons are coaxially disposed in a housing. The adjustment member comprises a threaded spindle and a threaded nut, whereby these form a frictional coupling with the hand brake piston by way of a conical surface, for example, in order that a mutual shortening of the coupling between the threaded spindle and the threaded nut during application of the hand brake is precluded. Upon application of the hydraulic foot brake a lengthening of the coupling is possible by rotation of the threaded nut, because the aforementioned frictional coupling is not engaged. The rolling bearing and the spring facilitate the rotational motion. Upon application of the hand brake, the adjustment member is radially fixed, on the one hand, by the automatically centered frictional coupling and, on the other hand, by the threaded spindle pressed securely in the base of the brake piston. In order that the rolling bearing arranged approximately in the center will in this way not be radially deformed, the outer ring is fixed, with the possibility of radial adjustment, between a surface attached to the housing and a spring. Depending upon the manufacturing tolerances or errors in assembly, in particular upon pressing of the threaded spindle in the brake piston, a large radial deformation of the threaded spindle can occur upon engagement of the frictional coupling, whereby also disadvantageous effects on the thread or on the sliding surface of brake piston can be anticipated. The same situation arises if conversely the threaded nut is connected to the piston and the frictional coupling is arranged on the threaded spindle.